College

Quillan began his collegiate career for the Quinnipiac Bobcats during the 2021–22 season, where he recorded two goals and seven assists in 37 games.^[1] He scored his first career goal on October 26, 2021, in a game against Holy Cross.^[2]

During the 2022–23 season, in his sophomore year, he recorded 19 goals and 19 assists in 41 games. During the Frozen Four at the 2023 NCAA Division I men's ice hockey tournament, Quillan scored two goals in a victory over Michigan and help Quinnipiac advance to the national championship game.^[3][4] During the championship game, he scored the game-winning goal ten seconds into overtime to defeat Minnesota and win the program's first NCAA title.^[5][6] He finished the NCAA Tournament with five goals, setting a new program record for goals in a single tournament, surpassing the previous record of four set by Matthew Peca in 2013.^[7] He was subsequently named the tournament Most Outstanding Player.^[8][9] During the 2023–24 season Quillan recorded 17 goals and 29 assists in 39 games. He recorded ten goals and 20 assists in 22 conference games, for a 1.36 points per game average. Following the season he was named an All-ECAC Second Team selection and ECAC Hockey Best Defensive Forward.^[10][11] He finished his collegiate career with 38 goals and 55 assists in 116 NCAA games.^[12]

Professional

On April 1, 2024, Quillan signed a two-year, entry-level contract with the Toronto Maple Leafs.^[13][14]